View
227
Download
1
Category
Preview:
Citation preview
8/9/2019 Modern Portfolio Theory-Markowitz
1/15
Modern Portfolio Theory
Prof Mahesh KumarAmity Business School
8/9/2019 Modern Portfolio Theory-Markowitz
2/15
Modern Portfolio Theory
Harry Markowitz William F. Sharpe Merton Miller
Modern portfolio theory was introduced by HarryMarkowitz in 1952. Markowitz, Sharpe & Miller were co-recipients of the Nobel Prize in Economics in 1990 fortheir pioneering work in portfolio theory
8/9/2019 Modern Portfolio Theory-Markowitz
3/15
Expected ReturnThe expected return on a portfolio is the weightedaverage of the returns of each asset within theportfolio
Example: A portfolio is comprised of three securitieswith the following returns:
Security Return % of Portfolio
A 5% 30%B 10% 45%
C 15% 25%
8/9/2019 Modern Portfolio Theory-Markowitz
4/15
Expected ReturnThe expected return of the portfolio is theweighted average:
!
!
!
!
n
j j j 1
r r
. 1 0 % . 1 5 % . 5
9 . 7 5 %
r j = retur n at time period j= expected retur n
w j = proportio n of the portfolio comprised of asset jr
8/9/2019 Modern Portfolio Theory-Markowitz
5/15
Portfolio Risk: Two Risky AssetsStandard deviation of a two-asset portfolio iscalculated as follows:
A A A A, A = w + w + w w
A
A,
= standard deviation
w = the proportion of the portfolio comprised of A = the correlation coefficient between A &
8/9/2019 Modern Portfolio Theory-Markowitz
6/15
Portfolio Risk: Two Risky Assets
2 2 2 2A A B B A B A,B A B= w + w + 2w w
Portfolio risk is driven mainly by thecorrelation between the assets!!
8/9/2019 Modern Portfolio Theory-Markowitz
7/15
CorrelationCorrelation is a measure of the linear relationshipbetween two assets
Correlation varies between perfect negative (-1) toperfect positive ( 1)Perfect negative correlation: when the return onasset A rises, the return on Asset B falls and viceversaPerfect positive correlation: the returns on asset Aand Asset B move in perfect unison
8/9/2019 Modern Portfolio Theory-Markowitz
8/15
Correlation & Risk Reduction B
ARA
A B
RBPerfectNegative Correlation
PerfectPositive Correlation
Less thanPerfect Correlation
To minimize portfolio risk, choose assets that havevery low correlations with each other.
8/9/2019 Modern Portfolio Theory-Markowitz
9/15
Moving Toward Many Risky AssetsWhen the portfolio consists of many risky assets,they form a plot similar to a broken egg shellshapeEach dot within the broken egg shell shaperepresents the risk/return profile for a single riskyasset or portfolio of risky assetsTo maximize return per unit of risk assumed, aninvestor would always choose an asset or portfoliothat plots along the efficient frontier
8/9/2019 Modern Portfolio Theory-Markowitz
10/15
Portfolios: Many Risky Assets
YouYou wouldwould nevernever choosechoose AssetAsset A,A, asas youyou cancan earnearn a a higherhigher returnreturnwithwith similarsimilar riskrisk byby choosingchoosing the the assetasset thatthat plotsplots alongalong thethe EfficientEfficientFrontierFrontier. .
RA
A
Return
Standard Deviation
A
8/9/2019 Modern Portfolio Theory-Markowitz
11/15
Choosing a Portfolio: So FarThe investor first decides how much risk toassume
The investor then chooses the portfolio thatplots along the efficient frontier with thatamount of risk
8/9/2019 Modern Portfolio Theory-Markowitz
12/15
Introducing the Risk Free Security
When a risk-free asset (Treasury Bill) isintroduced into the set of risky assets, a new
efficient frontier emergesThis new efficient frontier is known as theCapital Market Line (CML)The CML represents all possible portfolioscomprised of Treasury Bills and the MarketPortfolio
8/9/2019 Modern Portfolio Theory-Markowitz
13/15
Adding the Risk-Free Asset
RM
M
Return
Standard Deviation
A
Rf
Capital Market Line
8/9/2019 Modern Portfolio Theory-Markowitz
14/15
Capital Market Line (CML)
To maximize return for an amount of risk, investors shouldhold a portion of their assets in T-bills and a portion in themarket portfolio.
Linear relationship between risk and returnTo earn an expected return greater than the return on themarket portfolio, invest more than 100% of ones own wealthin the market portfolio.
PortfolioW ell-d iversified f M arket f Portfolio Market
R = r r - r
8/9/2019 Modern Portfolio Theory-Markowitz
15/15
What are we Missing?We know:
I nvestors should split their assets betweenTreasury bills and the market portfolioTo reduce risk, invest a greater proportion of assets in Treasury billsTo enhance expected return, invest a greaterproportion of assets in the market portfolio
Recommended